Thee value of the function f(2) is 70
What is a function?A function can be defined as an expression, law or rule that stands to explain the comparison between two variables.
These are namely;
The independent variableThe dependent variableFrom the information given, we have the function as;
f(x)=(3x-1)(2x+10)
To determine the value of the function when x = 2, we have to substitute the value of x as
Now, substitute the value into the function, we have;
f(2) = (3(2) - 1 )(2(2) + 10)
expand the bracket
f(2) = (6 -1)(4 + 10)
Add or subtract the values
f(2) = (5)(14)
Multiply the values, we have
f(2) = 70
Hence, the value is 70
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You are making several purchases from the I.B. Electric electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. Using this information and the information below, which way would you save the most money?
15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.
Which way would you save the most money?$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.
Let's say the entire amount spent was $100.
In a physical store, 100 times 15% equals 15 off.
100 - 15 = 85 is the item's reduced cost.
85 x 6% is 5.1 sales tax.
85 + 5.1 = 90.10 as a whole price
Internet shop:
Discounted cost of item: 100 - 5 = 95
95 plus 8.99 is 103.99 in total.
15% discount; 6% sales tax in-store.
Online retailer: $5 discount; $8.99 for delivery.
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Find the angle round to the nearest degree. please help.
63 degrees is the angle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angle triangle.
The opposite side length is 85 and the adjacent side is 38.
Opposite side=85
Adjacent side=38.
Calculate Opposite/Adjacent
= 85/38= 2.236
Which is tanθ=2.236
Now tan inverse on both the sides
θ=tan⁻¹2.236
θ=tan⁻¹2
θ=63 degrees.
Hence, the angle is 63 degrees.
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Allie receives a $20 gift card for the local coffee shop, where she only buys lattes and muffins. If the price of a latte is $4 and the price of a muffin is $2, then we can conclude that Julia:
If the price of a latte is $4 and the price of a muffin is $2, then we can conclude that Julia can buy 5 lattes or 10 muffins ($20) if she chooses to buy only one of the two goods.
How to illustrate the price?A price is the sum of money that one party pays or receives in exchange for another's goods or services. The cost of production may go by another name in certain circumstances. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price."
In this case, Allie receives a $20 gift card for the local coffee shop, where she only buys lattes and muffins. Here, we can conclude that Julia can buy 5 lattes. This will be 5 × $4 = $20 or 10 muffins which will be:
= 10 × $2
= $20
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The area of ground A is given by 12x^2y sq. units and the area of ground B is given by 6xy^2sq Units
where x>0 and y> 0. Tiles of the same size need to be installed on both the grounds. What should
be the maximum tile area so that it can be used for both the grounds?
The maximum area of the tile to contain both grounds is 12x²y²
How to determine the maximum area of the tile?From the question, we have the following parameters that can be used in our computation:
Area of ground A = 12x^2y sq. units
Area of ground B = 6xy^2sq units
Rewrite these areas properly
So, we have the following representation
Area of ground A = 12x²y sq. units
Area of ground B = 6xy² sq units
Express the areas as the products of their prime factors
This gives
Area of ground A = 2 * 2 * 3 * x * x * y
Area of ground B = 2 * 3 * x * y * y
From the above products, we have
Least common multiple = 2 * 2 * 3 * x * x *y * y
Evaluate the products
Least common multiple = 12x²y²
This represents the greatest area
Hence, the greatest area is 12x²y²
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lens $50000 over three months payable weekly at interest rate pf 2.85 per week should the person be late charge $600 per week. since the customer was late 5 times during the life of the loan and took and took an additional 2 weeks to settle calculate thr total interest
The total interest paid on the loan repayable over three months weekly at 2.85% per week is $3,584.96.
How is the total interest determined?The total interest can be computed using an online finance calculator.
The result is then added to the late payment fees. The default payment fee is the product of $600 and 5.
N (# of periods) = 14 weeks (3 x 4 + 2)
I/Y (Interest per year) = 2.85%
PV (Present Value) = $50,000
PMT (Periodic Payment) = $4,000
Results:
Sum of all periodic payments = $56,000.00
Total Interest = $584.96
Late payment charge = $3,000 ($600 x 5)
Total interest and late charge = $3,584.96
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Question Completion:Assume that the borrower repays $4,000 weekly.
Find f(x) where f'(x)=4x+7
Answer:
[tex]2x^2+7x+C[/tex]
Step-by-step explanation:
Find the antiderivative of f'(x)=4x+7
[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]
if you apply demorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))), you get:
Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).
DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).
Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).
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determine whether the lines are parallel, perpendicular, or neither L1: y= -2/3x-3, L2 y= -2/3x+6
The two linear equations have the same slope, -2/3, and different y-intercepts, thus, the lines are parallel.
Are the lines parallel, perpendicular or neither?A general linear equation is written as:
y = a*x +b
Where a is the slope and b is the y-intercept.
Two linear equations are parallel if both lines have the same slope and different y-intercepts.
And two lines are perpendicular if the product between the slopes is equal to -1.
In this case, we have the two linear equations:
y= -(2/3)*x - 3
y= -(2/3)*x + 6
So you can see that both linear equations have the same slope -2/3 and different y-intercepts, thus, the lines are parallel.
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An alternative sampling method would be to select a stratified random sample of eight apartments, where the
strata are apartments with children and apartments with no children. A stratified random sample of size eight
might include two randomly selected apartments with children and six randomly selected apartments with no
children. In the context of this situation, give one statistical advantage of selecting such a stratified sample as
opposed to a cluster sample of eight apartments using the floors as clusters.The amount of carpet wear could be different for apartments with and without children.
2. The stratified random sample ensures that some apartments with children will be selected.
(a) There are 36 ways to select 8 apartments randomly by cluster sampling method.
(b) Throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.
(a) Given the building has 9 floors which are taken as N=9 clusters.
Each floor has 4 apartments.
It is to select 8 apartments by cluster sampling method.
That is to select a sample of size any n=2 floors(clusters) by cluster sampling method out of the population of N=9 clusters.
By simple random sampling without replacement, there are NCn = 9C2 =36 ways to select 2 clusters.
Hence, there are 36 ways to select 8 apartments randomly by cluster sampling method.
(b) The main benefit of stratified sampling over cluster sampling is that the sample obtained using this method will unquestionably include representations of both features, i.e., apartments with and without children as a full representative of the population.
In contrast, there is no guarantee that the sample of flats with and without children from the cluster sampling approach will accurately reflect both qualities. Sometimes throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.
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The right question is given beow:
Express the following fraction in simplest form, only using positive exponents.
\frac{3a^9r^{-3}}{-4(a^2)^{-1}}
−4(a
2
)
−1
3a
9
r
−3
The simplified expression of the fraction in its simplest form is -12a¹¹r⁻³
How to express the fraction expression in its simplest form?From the question, we have the following parameters that can be used in our computation:
\frac{3a^9r^{-3}}{-4(a^2)^{-1}}
Rewrite the above expression properly
So, we have the following representation
3a⁹r⁻³/(-4a²)⁻¹
Evaluate the expression in bracket
So, we have the following representation
3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * (-4a²)
Remove the brackets
This gives
3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * -4a²
Evaluate the products
So, we have the following representation
3a⁹r⁻³/(-4a²)⁻¹ = -12a¹¹r⁻³
Hence, the the fraction expression in its simplest form is -12a¹¹r⁻³
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Can anyone help me ASAP?
Write as a single fraction in its simplest form.
[tex] \frac{ {x}^{2} - 3x}{ {x}^{2} - 9 } [/tex]
Answer:
[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]
[tex]\frac{x}{x+3}[/tex]
suppose a die is tossed 1000 times, and the following frequencies are obtained for the number of pips up when the die comes to a rest. x1 x2 x3 x4 x5 x6 163 178 142 150 183 184 using the chi-squared goodness of fit test, assess whether we have evidence that this is not a symmetrical die. record the standardized residuals.
We have evidence that this is not a symmetrical die, the standardized residuals is 9.5689
The die is tossed 1000 times
Given the observed value
x1 = 163
x2=178
x3=142
x4= 150
x5 = 183
x6 = 184
The mean = 163 + 178 + 142 + 150 + 183 + 184 / 6
= 1000 /6
= 166.67
Next we have to find the value of (observed value - Expected value)^2 / Expected value
x1 = (163-166.67)^2 / 166.67 = 0.081
x2 = (178-166.67)^2 / 166.67 = 0.7659
x3 = (142-166.67)^2 / 166.67 = 3.6598
x4 = (160 -166.67)^2 / 166.67 = 1.673
x5 = (183 - 166.67)^2 / 166.67 = 1.5938
x6 = (184-166.67)^2 / 166.67 = 1.7954
The standardized residuals = 0.081 + 0.7659 + 3.6598 +1.673 +1.5938 +1.7954 = 9.5689
Therefore, this is not a symmetrical die
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A scientist began measuring the temperature of a solution when it was 100 °F. The temperature of the solution
decreased at a constant rate of 1.5 °F per hour.
Which function can be used to find y, the temperature of the solution in degrees Fahrenheit after x hours?
Ay 1.5x - 100
By 1.5x + 100
y 100x1.5
Oy - 100x + 1.5
Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.
The required details for Conditional problems in given paragraph
This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.
For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.
The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.
what are conditional problems?
Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.
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Find the dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2. (Let x, y, and z be the dimensions of the rectangular box.)(x, y, z) =
The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
Given that:
Total surface area of the rectangular box or cuboid = 100 cm²
A rectangular box with largest volume is a cube.
The total surface area of a cube = 6 times square of one edge length.
Let the edge length = given dimensions; x, y, z
So,
x = y = z
6x^2 = 100
x^2 = 100 / 6
x = √ 100 / 6
x = 10 / √ 6 cm
x = 2.449 cm
Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
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Given a binomial experiment with the probability of success on a single trial p = 0.80, find the probability that the first success occurs on trial number n = 3. (Round your answer to three decimal places.)
The probability that the first success occurs on trial number n = 3 is 0.032
How to find the probability that the first success occurs on trial number n = 3?Given:
probability of success on a single trial p = 0.80
trial number, n = 3
Recall the formula for the Geometric Probability Distribution
P(n) = p(1 - p)ⁿ⁻¹
where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial
P(n) = p(1 - p)ⁿ⁻¹
P(3) = 0.8(1-0.8)³⁻¹
P(3) = 0.8(0.2)²
P(3) = 0.032
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emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28% sophomores: 26% juniors: 24% seniors: 22% according to the information emily has gathered, which of the following statements are true? choose all that are correct. responses more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15.
The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
Given :
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 % .
Freshmen = 0.85
sophomores = 0.80
it is clearly visible that the freshmen or sophomores is greater than the 40 % .
Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
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I need help with this please help me
The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).
What does a math translation mean?Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.
What does math formula translation mean?Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.
Briefing:The image of the translation is (9,-2).
The point is given as: P = (-6, -4)
The image of the point is: P' = (-2, 3)
The translation rule is calculated as:
T = x - 2 - (-6), y+3-(-4)
so, T = x + 4, y + 7
So, the image of (5, -1) is:
the Image of the translation = 5 + 4, -1 + 7
Hence, the image of the translation is (9, 6).
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What values of x make the two expressions below equal?
(x-1)(x-6)_
4(x-1)
x-6
4
A. All real numbers except 1
B. All real numbers except 6
C. All real numbers
D. All real numbers except 1 and 6
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expressions are given below.
[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4
Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have
⇒ [(x - 1)(x - 6)] / [4(x - 1)]
⇒ (x - 6) / 4
But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
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A _______ is a set of input data in a relationship
The complete answer: A domain is a set of input data in a relationship.
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
An input value and an output value are matched in a relation.
A relation is a function where each input value yields one and only one output value.
Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,
while the range is the set of output values.
The domain of a function or relation is the set of all possible independent values that it can have.
Therefore, a domain is a set of input data in a relationship.
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build a slope intercept equation with given information (1,3); m=3
The Slope intercept form of equation passing through points ( 1 , 3 ) and having slope 3 is y = 3x
What is Slope Intercept Form ?In mathematics, formulating an equation for a line in the form y = mx + b is known as slope intercept form. The m stands for the line's slope, and the b for the y-intercept. When you need to find a point on a line or solve for y given x, you utilize the slope intercept form.
According to the given information
Form of the slope intercept: y = mx + b
It goes through some points ( 1 , 3 )
Slope of the line given m = 3
Put x = 1 and y = 3 and m = 3 in slope intercept form equation
3 = 3( 1 ) + b
b = 0
Hence
Put the value of b = 0 in y = mx + c
y = 3x
The Slope intercept form of equation passing through points ( 1 , 3 ) and having slope 3 is y = 3x
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Find the x and y intercepts of the line: 3x - 4y = -24
Answer:
x- intercept = - 8 , y- intercept = 6
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
3x - 4(0) = - 24
3x = - 24 ( divide both sides by 3 )
x = - 8 ← x- intercept
to find the y- intercept let x = 0 in the equation and solve for y
3(0) - 4y = - 24
- 4y = - 24 ( divide both sides by - 4 )
y = 6 ← y- intercept
The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
Answer:
2x² +5
Step-by-step explanation:
You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.
AreaThe area is the product of length and width, so the width will be ...
A = LW
W = A/L = (2x³ +6x² +5x +15)/(x +3)
The cubic expression can be factored by grouping, so we have ...
Area = (2x³ +6x²) +(5x +15)
= 2x²(x +3) +5(x +3)
= (2x² +5)(x +3)
Then the width is ...
[tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]
The width of the rectangle is 2x² +5.
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consider all postive interges that are multiples of 20 and that are less than or equal to 300. what fraction of those interges are multple of 15
Answer:
1/3
Step-by-step explanation:
Every third multiple of 20 is a multiple of 15.
your goal is to generate a simple math quiz with a number of equations that will be determined by the user. you will prompt the user for an answer to each equation and display whether they answered it correctly or incorrectly. at the end of the math quiz, you will display the number of total equations that they answered correct out of how many were given
The statement of the problem has already made a lot of decisions for us. We are told to use three global variables of type int[]. The variables must be static, and I have chosen to make them private, so the declarations become:
private static int[] firstNumbers; // The first numbers in all ten questions.
private static int[] secondNumbers; // The second numbers in all ten questions.
private static int[] user answers; // The user's answers to the ten questions.
Note that these declarations are not in any subroutine. These statements only create variables, not arrays. We still need to create three arrays of length 10. The arrays can be created using the new operator. This initialization could in fact be combined with the declaration of the variables:
private static int[] firstNumbers = new int[10];
private static int[] secondNumbers = new int[10];
private static int[] userAnswers = new int[10];
Another possibility would be to create the three arrays at the beginning of the main() routine. In fact, I chose to create them in the subroutines where they are first used.
The program has three stages -- create the problems, administer the quiz, and grade the quiz -- and we are told to write a subroutine to do each stage. The main program simply has to call the subroutines:
public static void main(String[] args) {
createQuiz();
administerQuiz();
gradeQuiz();
}
This is an example of using subroutines to break up a large task into several simpler subtasks, so that programming each subtask becomes a separate problem. The subroutines are short and not too hard to write. Looking at administerQuiz() as an example, note that the user's answers have to be stored in the array, the user answers so that they can be used when grading the quiz. I create the array itself before asking any questions and then store the user's responses in the array as they are read by the user. On the other hand, the arrays that hold the numbers that occur in the questions have already been created and filled before administerQuiz() is called. Here's the subroutine:
private static void administerQuiz() {
userAnswers = new int[10];
for (int i = 0; i < 10; i++) {
int questionNum = i + 1;
System.out.printf("Question %2d: What is %2d + %2d ? ",
questionNum, firstNumbers[i], secondNumbers[i]);
userAnswers[i] = TextIO.getlnInt();
}
}
A couple notes about the output: I wanted to number the questions 1, 2, ..., 10, but the elements of the arrays are numbered 0, 1, ..., 9. This means that the question number that I output has to be one more than the array index. Also, all the numbers that occur in my program are either one or two digits. By allowing exactly two digits for each number in the output, I can get everything to line up neatly. Here's the I/O for a sample run of the program:
Welcome to the addition quiz!
Question 1: What is 40 + 14 ? 54
Question 2: What is 18 + 38 ? 46
Question 3: What is 21 + 31 ? 52
Question 4: What is 18 + 36 ? 54
Question 5: What is 43 + 12 ? 55
Question 6: What is 21 + 17 ? 38
Question 7: What is 33 + 25 ? 58
Question 8: What is 39 + 21 ? 70
Question 9: What is 1 + 25 ? 26
Question 10: What is 39 + 26 ? 65
Here are the correct answers:
Question 1: 40 + 14 = 54. You were CORRECT.
Question 2: 18 + 38 = 56. You said 46, which is INCORRECT.
Question 3: 21 + 31 = 52. You were CORRECT.
Question 4: 18 + 36 = 54. You were CORRECT.
Question 5: 43 + 12 = 55. You were CORRECT.
Question 6: 21 + 17 = 38. You were CORRECT.
Question 7: 33 + 25 = 58. You were CORRECT.
Question 8: 39 + 21 = 60. You said 70, which is INCORRECT.
Question 9: 1 + 25 = 26. You were CORRECT.
Question 10: 39 + 26 = 65. You were CORRECT.
You got 8 questions correct.
Your grade on the quiz is 80.
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City A is located in a valley 15 meters below sea level, and City B is located *
43 meters above sea level. What is the difference, in meters, between the
elevations of these two cities? Remember, difference means subtract (and
you will need to SCO).
Answer:
To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.
Consider the vector function given below. r(t) = (9t, 4 cos(t), 4 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) N(t) = (b) Use this formula to find the curvature. k(t) = Consider the following vector function. r(t) = (2V2t, ezt, e-2t) (a) Find the unit tangent and unit normal vectors T(t) and N(t).
From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
(a) To find the unit tangent and unit normal vectors, we use the following formula:
T(t) = (1/|r'(t)|) * r'(t)
N(t) = (1/|r'(t)|) * (r'(t) x r"(t))
where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.
For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).
Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))
To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).
Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))
and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).
(b) To find the curvature, we use the following formula:
k(t) = |r'(t) x r"(t)| / |r'(t)|3
For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).
Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3
= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
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log base (2) of (x^2 +5) = (3)
Answer:
Step-by-step explanation:
log base (2) of (x^2 +5) = (3) can also be described as 2^3 = x^2 + 5
simplify: 8 = x^2+5
Subtract 5 from each side: 3 = x^2
square root: x = sqrt(3)
Answer:
Step-by-step explanation:
[tex]log(2)^{(x^2+5)}=3\\[/tex]
[tex]2^3 =x^2+5\\8-5=x^2\\x^2=3\\x=\pm\sqrt{3}[/tex]
which are prime polynomials
-12f+21
f-36
-3f-23
5f+10
Answer:
f - 36
-3f - 23
are your prime polynomials.
8w-16 how do i answer this
The factor of the expression 8w - 16 will be 8 and (w - 2).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.
The expression is given below.
⇒ 8w - 16
The factor of each term in the expression, then we have
8w = 8 x w
16 = 8 x 2
Then the expression is written as,
⇒ 8w - 16
⇒ 8 × w - 8 × 2
⇒ 8 × (w - 2)
⇒ 8(w - 2)
The component of the articulation 8w - 16 will be 8 and (w - 2).
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